Wavefront detection and analysis are desirable for many applications. For example, telescopes and other optical sensing systems desirably measure an optical wavefront in an accurate fashion. Additionally, directed energy weapons, such as high energy lasers and the like, often require an associated optical sensing system for detecting the optical wavefront returning from a target. In addition to astronomy and directed energy weapons systems, a number of other applications utilize or will utilize optical wavefront detection including scientific measurement systems, optical communications systems (such as those utilizing free space lasers) and medical imaging including vision correction, ophthalmology and microscopy.
An optical sensing system generally determines the phase of the optical wavefront. By analyzing the phase of the optical wavefront, sources of optical disturbances can be characterized. For example, common sources of optical disturbances include atmospheric turbulence or other disturbances in the atmospheric path. Additionally, the phase of an optical wavefront can help to characterize the optical system itself, such as for diagnostic purposes. In this regard, the phase of the optical wavefront can provide the information identifying imperfections in the optics, imperfections with the laser or the like. In addition to merely identifying the optical disturbances and/or characterizing the optical system, the wavefront measurement can be utilized to provide wavefront compensation, such as by reshaping a deformable mirror, by post-processing the optical signals or both.
A typical optical sensing system includes a collection telescope and a wavefront sensor for receiving an optical image that is directly related to and that characterizes aspects of the field at the collection telescope. Conventional wavefront sensors include Shack-Hartmann sensors and Shearing sensors. By way of example, a Shack-Hartmann sensor includes an array of lenses and a charge coupled device (CCD) camera. The array of lenses effectively divides the optical wavefront into a plurality of subapertures. The output of each lens is directed onto a plurality of pixels of the CCD camera. In one common embodiment, the output of each lens is directed onto a group of sixteen pixels, generally arranged in a four-by-four block and said to be associated with the subaperture.
As known to those skilled in the art, a wavefront sensor, such as a Shack-Hartmann sensor, typically determines the wavefront gradient for each subaperture. Based upon the gradients, the phase of the optical wavefront may be determined. The most common approach, as known to those skilled in the art, is to make the phase a least squares fit to the measured gradients. This approach is implemented by multiplying the gradients by a precomputed matrix, which associates the gradient measurements with various parts of the wavefront. In one much discussed enhancement to this approach to determining the phase of the wavefront, a weighted least squares reconstruction technique is employed in which the gradients of the optical wavefront are weighted to emphasize the impact of those gradients predicted to be the most accurate and having the highest information content. A common method is to assign a weight to a gradient that equals the average intensity of the portion of the optical wavefront captured by the respective subaperture raised to some power. This average intensity is proportional to the sum of the values of the CCD pixels corresponding to the subaperture, minus any background level. Alternatively the value of the maximum pixel in the subaperture region can serve as a similar measure to be assigned as a weight. Note that for weighted least-squares methods the important feature is the relative magnitudes of the weights to each other, e.g. multiplying all weights by some positive constant would not influence the solution. Processing-time considerations have heretofore limited the actual implementation of said approach, but a recent reformulation of the weighted least squares technique as a Lagrange constraint problem has put it in a form susceptible to rapid Cholesky decomposition techniques. See, for example, D. R. Gerwe, “Closed Loop Control for Adaptive Optics Wavefront Compensation in Highly Scintillated Conditions”, SPIE Proc. 5087 (2003).
Based upon the phase of the optical wavefront, the optical sensing system can address the effect of any optical disturbances, such as atmospheric turbulence and imperfections in the optics. For example, the optical sensing system may include a deformable mirror that is controllably deformed in response to the detected phase of the optical wavefront to accommodate or offset the effect that optical disturbances have had on the optical wavefront. In addition to or instead of the controlled deformation of a deformable mirror, the optical sensing system may subject the signals representative of the optical wavefront to post processing to similarly reduce, if not eliminate, the effects of optical disturbances upon images or other measurements made by the optical system.
One type of optical disturbance that is particularly difficult to address is scintillation, that is, spatio-temporal fluctuations in the intensity of the optical wavefront. Scintillation generally induces three types of performance loss. One type of performance loss is directly associated with the scintillated intensity profile. For imaging applications this profile should ideally be flat, while for high-energy laser applications, the laser should ideally match this scintillated profile, but typically does not. The second type of performance loss relates to the degradation of the wavefront sensor itself. Optical wavefronts having increased scintillation generally have regions in which the intensity varies greatly. The quantity measured by a subaperture of a wavefront sensor is the spatial average of the phase or phase gradient within the subaperture region and weighted by the corresponding spatial distribution of the amplitude or intensity of the optical field. Increased scintillation therefore generally reduces the accuracy of the phase measurement of the optical wavefront. The third type of performance loss is associated with wavefront singularities. In this regard, optical wavefronts having increased scintillation generally have increased numbers of wavefront singularities, which are intensity nulls generally referred to as branch points. The performance losses associated with branch points depend on methods used to process the measurements. By way of example, FIG. 1 depicts the performance of various optical sensing systems, such as Shack-Hartmann (shack) and Schearing (shear) sensors, as expressed by the Strehl ratio, a common measure of the performance of an adaptive optics system, as a function of the Rytov number, a common measure of scintillation strength. As shown, the performance of the wavefront sensors decreases significantly as the Rytov number increases. As denoted by the legend associated with FIG. 1, the optical sensing systems may include either a Shack-Hartmann (shack) or shearing (shear) wavefront sensor and either a faceplate or conventional deformable mirror (CVDM) or a piston segment deformable mirror (PSDM) and may employ either a least squares reconstruction algorithm (LS) or a weighted least squares (WLS) reconstruction algorithm in which the gradients of the wavefront are weighted by some measure of the intensity of the wavefront.
Accordingly, optical sensing/wavefront processing systems are available that determine the phase of an optical wavefront and, based upon the phase, controllably position a deformable mirror and/or appropriately process the signals representative of the optical wavefront. However, the performance of these systems is somewhat degraded by scintillation. As such, it would be advantageous to design an optical sensing system that was tolerant of scintillation and that provided an accurate measurement of the phase of an optical wavefront even if the optical wavefront experienced scintillation, thereby permitting appropriate wavefront compensation to be provided, such as by means of properly shaping a deformable mirror or by properly processing the signals representative of the optical wavefront.